The final scene is just a fantasy of James' while he's on the bus.
The odds of him running into someone he knew as the first person he met in New York City of all places is astronomical, obviously. Plus the whole scene has a bit of a dreamlike quality to it, the rain falls in a very Hollywood romantic
way and the overall atmosphere is just too perfect. The scene of him on the bus is the last scene of reality in the film.
- James didn't just "run into" Em, he was looking for her. Hence not being surprised to see her and having something of a speech ready. As mentioned elsewhere he could well have found out where she was living ahead of time, from her dad most likely. As for atmosphere, while this may be a low-key, fairly realistic film, a film it remains. Films often have more appropriate atmospheres than real life. And anyway the both of them were still pretty awkward.
Columbus wasn't his real name, and we never do find out what it is.
Jesse Eisenberg plays a character in both films. The Squid and the Whale
takes place 1986 and Adventureland
takes place 1987.